Consider two vectors ~ A and ~ B and their re- sultant ~ A + ~ B . The magnitudes of the vectors ~ A and ~ B are, respectively, 13 . 2 and 6 . 1 and they act at 110 ◦ to each other.Find the magnitude of the resultant vector ~ A + ~ B .
A = 13.2[0o]
B = 6.1[110o]
R = 13.2+6.1*Cos110 + i6.1*sin110 =
11.11 + 5.73i
R^2 = 11.11^2 + 5.73^2 = 156.3
R = 12.50
To find the magnitude of the resultant vector ~ A + ~ B, we can use the magnitude formula for vectors.
The magnitude of a vector ~ V is given by:
|~V| = sqrt((Vx)^2 + (Vy)^2)
Where Vx is the x-component of the vector ~ V and Vy is the y-component of the vector ~ V.
First, let's find the x and y components of vector ~ A and ~ B.
For vector ~ A:
Magnitude = 13.2
Angle = 110 degrees
To find the x and y components, we can use the following trigonometric relationships:
Vx = |V| * cos(angle)
Vy = |V| * sin(angle)
For vector ~ A:
Vx = 13.2 * cos(110)
Vy = 13.2 * sin(110)
Similarly, for vector ~ B:
Magnitude = 6.1
Angle = 110 degrees
Vx = 6.1 * cos(110)
Vy = 6.1 * sin(110)
Now that we have the x and y components for both vectors ~ A and ~ B, we can add them together to get the x and y components of the resultant vector ~ A + ~ B:
Resultant Vx = VAx + VBx
Resultant Vy = VAy + VBy
Finally, we can calculate the magnitude of the resultant vector using the magnitude formula:
|~A + ~B| = sqrt((Resultant Vx)^2 + (Resultant Vy)^2)
By plugging in the values we calculated, we can find the magnitude of the resultant vector ~ A + ~ B.